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Module details

MA209-5-SP: INTRODUCTION TO NUMERICAL METHODS

Year: 2014/15
Department: Mathematical Sciences
Essex credit: 15
ECTS credit: 7.5
Available to year(s) of study:
Available to Study Abroad / Exchange Students: Yes
Full Year Module Available to Study Abroad / Exchange Students for a Single Term: No
Co-requisites: MA206-5-AU

Staff
Supervisor: Dr Hadi Susanto, email: maths@essex.ac.uk  
Teaching Staff: Dr Hadi Susanto, email: maths@essex.ac.uk  
Contact details: Miss Claire Watts, Departmental Administrator, Tel. 01206 873040, email cmwatts (Non essex users should add @essex.ac.uk to create the full email address) 

Module is taught during the following terms
AutumnnoSpringyesSummerno

Module Description

The module gives an introduction to practical techniques for carrying out numerical computations on a range of mathematical problems. Students will be expected to have an elementary acquaintance with Matlab. (An introductory session on Matlab will be provided for those who need it.)

1. An Introduction to Practical Computation

- Algorithms

- Simple examples

- Pitfalls

2. Solving single nonlinear equations

- Bisection Method

- Regula Falsi

- Newton's Method

3. Numerical linear algebra

- Gaussian Elimination

- Partial pivoting

- Iterative methods

4. Numerical solution of ordinary differential equations

- Euler's Method

- Runge-Kutta Methods

- Linear Multi-step Methods

5. Simple approximation

- Polynomial interpolation

- Optimal interpolation points

- Fourier and Trigonometric Series

On completion of the module students should be able to:

- appreciate the processes and pitfalls of mathematical approximation

- demonstrate knowledge and understanding of mathematical computing

- motivate and describe the derivation of the numerical algorithms covered in the module

- carry out simple numerical processes "by hand"

- implement and execute algorithms in Matlab

- evaluate, contrast and reflect upon the numerical results arising from different algorithms.

Learning and Teaching Methods

This module runs at 3 hours per week in the Spring term. There are two lectures and one class / laboratory each week. In the Summer term 3 revision lectures are given.

Assessment

30 per cent Coursework Mark, 70 per cent Exam Mark

Coursework:
The coursework will involve five practical assignments, one associated with each of the five major headings in the module description above.

Other details:
Information about coursework deadlines can be found in the "Coursework Information" section of the Current Students, Useful Information Maths web pages: Coursework and Test Information

Exam Duration and Period

2:00 hour exam during Summer Examination period.

Bibliography

  • Recommended reading
  • C. Moler, Numerical Computing with Matlab. SIAM (2004).
  • Supplementary reading
  • B. Bradie, A Friendly Introduction to Numerical Analysis. Prentice-Hall (2005).
  • J. Mathews and K. Fink, Numerical Methods using Matlab, (4th ed.) Prentice-Hall (2004).

Further information

Should you have any queries about the Module Directory pages, please contact the Course Record Team, Systems Administration Office, Academic Section; email: crt (non Essex users should add @essex.ac.uk)